Electromagnetic tool using slotted point dipole antennas

ABSTRACT

An electromagnetic tool using slotted dipole antennas is presented. The dipoles may be placed in slots on a drill collar. A receiver or transmitter antenna consists of one or more slots. A dipole consists of a ferrite rod with electric wires placed above and below the ferrite. Wires may be connected such that wire current forms a loop around the ferrite rod. When a group of slots are used for an antenna, wire holes are constructed between slots. Effectively a single wire may be used to go above all ferrite rods in the group and then turn to go below all the rods. Two wire segments are in a wire hole connecting two adjacent slots. Currents in the two segments are the same in magnitudes and flow in opposite directions. There is no net current in wires in a wire hole.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application incorporates by reference the entire provisionalapplication identified by U.S. Ser. No. 62/926,808, filed on Oct. 28,2019, and claims priority thereto under 35 U.S.C. 119(e).

BACKGROUND

In recent years, information on the property of formation traversed by awell bore is gathered during the drilling process in oil and gas wells.The information is used to evaluate the geological properties of theformation. Lately, the information is also used, often times exclusivelyor predominantly, for determining the position of the well section beingdrilled relative to the Earth formation geological structure. Thepositional information relative to the geology is used in deciding thenext course of action in the drilling process in order to place the nextsection of the well in a zone of hydrocarbons to maximize production.The process of measuring formation parameters while drilling and thenusing the measurements to determine the formation structure relative toa borehole to aid the steering of a well is called geological steering,or geosteering. The regional Earth formation geological structure istermed formation structure or formation. Two formations are differenteven if the geometrical shapes are identical but one or more geometricalvolumes have different geologies. Hereafter, formation properties orformation parameters comprises geological properties, geometricalstructure information, and relative position between a well section andformation geological structure.

The measurement of formation properties while a well is being drilledwas first called Formation Evaluation Measurement While Drilling(FEMWD). Later the term Logging While Drilling (LWD) was used.

One of the formation properties measured by a LWD system is resistivity.This parameter quantifies how difficult it is to conduct electriccurrent in the formation. The porous space in a potential hydrocarbonbearing formation is filled with either hydrocarbon fluid or brine.Hydrocarbon fluid, namely oil and gas, is strongly resistive, whilebrine is conductive. By measuring resistivity, an estimation of what thepercentage of porous space having oil and gas in a well section in ahomogenous formation may be determined.

Wave propagation resistivity tools have been used for LWD resistivitymeasurement. Transmitter antennas and receiver antennas are built onto asection of a drill collar. Electromagnetic waves are transmitted from atransmitter antenna of a tool into a borehole. The wave propagatesthrough the space including both the borehole environment and formationsurrounding the borehole. The wave signal at the receiver antennalocated on the drill collar some distance away from the transmitter ismeasured. The phase delay and amplitude attenuation of the receiver wavesignal relative to those of the transmitter are obtained from themeasurement of the wave signal at a receiver when one transmitter istransmitting at a frequency. The phase delay may be referred to asphase. The amplitude attenuation may be referred to as attenuation oramplitude. The phase and attenuation are functions of frequency,distance between the transmitter and receiver, the borehole geometry andits property, and the electromagnetic properties of the formation nearthe borehole.

In electronics, the term ‘gain’ is used to mean a scale factor in powerlevel and a shift in phase. The scale factor can be larger than orsmaller than 1. A gain is often represented by a complex number. Ingeneral, amplifying or attenuating systems are often used in the signalgeneration or signal detection processes. The gains are generated toimprove signal quality and measurement accuracy. There are uncontrolledgains in transmitters and receivers which come from the antennastructure and circuitry. The uncontrolled gains can also come fromerrors in amplification or attenuation systems which deviate fromdesigned behavior. Unless specifically noted otherwise hereinafter theterm gain or gains means only the uncontrolled gain or gains

In addition to being affected by borehole and formation parameters, thephase and attenuation measurement is also affected by gains in thetransmitter and the receiver. With digital electronics, a transmitter iscommanded to turn on with a known power level and phase. The actualpower level and phase in the transmitter are shifted by the gain in theanalog portion of the antenna that transmits electromagnetic waves.Similarly, between the wave signal at a receiver location and theanalog-to-digital conversion stage of the receiver system there is again. The gains drift with temperature. In earlier resistivity toolswith mostly analog electronics, the gains and associated shifts are evenmore pronounced. The nominal phase value of a transmitter signal isn'tknown with analog electronics. The range of frequency used by and thegeometry of the antennas on resistivity tools are such that theradiation resistance of an antenna is relatively small. The uncontrolledgain variation in an antenna depends mostly on minute variations in thestructure of the antenna and the properties of the electronic componentsand materials used in the antenna. The gain drifts greatly in thetemperature range experienced by a resistivity tool. The gain can benon-repeatable from antenna to antenna and are not easily tracked andcalibrated. The effects of the gains on phase and attenuation must beremoved in order to extract information about formation properties.

Multiple transmitter-receiver pairs operating at one or multiplefrequencies are used to create measurement combinations. Eachcombination is designed to be mostly sensible to a particular propertyof a particular region near a resistivity tool. For example, a LWDresistivity tool used in drilling operations can include one transmitterand two receivers. The two receivers are closely spaced and are somedistance away from the transmitter along the axis of the tool that ispart of the drill string. When the transmitter is powered on, the phasedifference and amplitude ratio between the signals at the receivers aremostly sensitive to the resistivity of the formation region away fromthe borehole and are minimally affected by borehole properties in mostsituations. This desirable property is called borehole rejection in theindustry.

The combinations are also used to overcome imbalances or drifts inelectronics, namely the gains in transmitter and receiver antennas. Thedifferential measurements between a pair of receivers described in theprevious paragraph are unaffected directly by the transmitter powerlevel or phase. As long as the power level is above the signal-to-noiserequirement, the receiver differential measurements are free of theeffects of the transmitter gain. Therefore, there is no need tocalibrate the transmitter. The effect of gains common to the tworeceiver systems is also removed by the differential measurement.However, the gains in the two receivers may be different and driftdifferently with temperature. To overcome the effect of im-balances inthe receivers, a second transmitter with the same frequency is placed onthe side of the two receivers opposite to the first transmitter alongthe drill collar axis. Namely the two receivers are in between the twotransmitters. The phase difference and amplitude ratio between thesignals at a first receiver and a second receiver from the firsttransmitter are measured. Then the first transmitter is turned off andthe second transmitter on the other side of the receivers is turned on.The phase difference and amplitude ratio between the signals at thesecond receiver and first receiver are obtained. The two phasedifferences in degrees and the two amplitude ratios in dBs are averaged,respectively. The phase errors caused by the difference between tworeceiver gains are the same in magnitude in the two phase differencemeasurements, but are opposite in sign. The averaging of the two phasedifferences completely removes the error due to receiver gaindifference. The errors in amplitude ratios from the receiver gaindifference are removed in a similar fashion. The averaged phasedifference is called compensated phase difference, or compensated phase.The averaged amplitude ratio is termed compensated amplitude ratio, orcompensated attenuation. Even though the gains in antennas differ fromantenna to antenna and are very sensitive to temperature, the gain in aparticular antenna within a measurement cycle is very stable. There isno measurable difference in the gain in a receiver between a firsttransmitter and a second transmitter transmitting sequence in a boreholeenvironment where temperature changes slowly relative to the toolmeasurement cycle. The compensated measurements are free of the effectsdirectly due to gains in either the transmitters or the receivers.

Even though the systematic errors due to antenna gains are eliminated orgreatly reduced by measurement combinations such as compensated phaseand attenuation, the random noise in antenna electronics can causemeasurement errors. The common techniques of increasing signal-to-noiseratio and expanding signal averaging window are used in most LWD tools.An antenna is tuned to resonate at its operating frequency(s). Thisgreatly increases the signal level and narrows noise band. Thetransmitter power level is constrained by the limited power supplyavailable to the resistivity tool operation in a well. In addition,because LWD tools operate while the drill string is moving, the signalaveraging window needs to be small enough so that during a measurementcycle the tool only moves by a small amount. Further increases onsignal-to-noise ratio need to come from improvement in antenna design.

The raw tool measurements including measurement combinations areconverted into measurements of formation properties through conversionfunctions. The conversion functions are the inverses of the forward toolresponse functions. In very limited cases, a tool response functionconsists of a table of experimental data. Because the structure andgeology of formations encountered by a LWD resistivity tool can be verylarge in scale and complex, it may be impractical to build thecollection of experimental setups to obtain a tool's response in allthose environments. In most cases, the tool response functions or dataare generated by modeling how electromagnetic waves generated by atransmitter propagates in various borehole and formation structuresbased on the laws of physics governing the behavior of electromagneticwaves. For each borehole and formation structure, and for everytransmitter-receiver antenna pair in the tool, the receiver output iscomputed. The computed receiver's signals (i.e., receiver voltages orreceiver currents or receiver readings) from all the antenna pairs areprocessed and combined in exactly the same way as what is done in a toolfor each borehole and formation structure. The modeled tool responsesare compared with the tool measurements. A best match is determined. Theformation parameters in the model associated with the best match aredeemed to be the tool measurements.

The converted measurements are the output of the LWD system. They arethe tool measurements or data. The raw tool measurements such ascompensated phase and attenuation are considered as intermediate resultsof a resistivity tool. The final tool data are derived from theintermediate results.

The impracticality of building large number of experimental setups toobtain tool response functions is one reason on why theoretic modelingis used for computing tool response function to be used for dataconversion and interpretation. Another reason is that laboratoryexperimental setups may not accurately duplicate the environments a LWDresistivity tool experiences in a well. A LWD resistivity tool is aprecision instrument. The resolution on attenuation measurement achievedby several manufacturers is 0.0002 decibels (dBs) at up to 175 degreesCelsius. This equals to 23 parts per million. As such, the amplitudemeasurement of a receiver voltage needs to have five effective digits inmany cases. Similarly, the phase measurement also needs to have fiveeffective digits. The accuracy of the attenuation measurement achievedby some manufacturers are less than 0.005 dBs at temperatures to 175degrees Celsius.

In a well, a LWD tool is installed near the bottom of a drill string.For example, it can be a few meters to a few tens of meters from thedrill bit at the bottom. The length of the drillstring above theresistivity tool is approximately the entire length of the well that hasbeen drilled at the time. In zones where resistivity measurements areimportant, the length of a well can be a few hundred to a few thousandmeters. The tool is electrically well grounded even with resistiveoil-based drilling fluid in the well because the area of contact betweenthe drillstring and the Earth is very large. In the cylindrical modelused to compute tool response, the drillstring, borehole, and formationsare assumed to be extending in the axial direction of the well sectionnear the tool indefinitely in both directions. The tool is assumed to beperfectly grounded with its surroundings in the model. In terms ofgrounding, the model ideally matches the environment in which a LWD toolis operating during the drilling process.

In a laboratory, the Earth formation is often simulated by a tank ofwater. The resistivity of the water is determined by its salinity. Thetank resistivity is often chosen to be at the lowest limit of thedesigned resistivity range. The limit often is at or close to 0.2 Ohm-M.Salt is added to the water to reach this resistivity. For a giventransmitter power, the receiver signal is the lowest at this limit. Themost challenging signal-to-noise-ratio point is a good test for anytool. At this resistivity the size of the tank required to simulate theinfinite Earth formation is also the smallest because electromagneticsignals attenuate faster in more conductive (less resistive) medium. Thetool section alone with its limited length is immersed into the middleof the tank vertically to simulate the tool in a formation as part of analmost infinitely long drillstring. Without any borehole structure, thetool surface is in good electric contact with the body of salty water inthe tank. The tool section itself can be considered to be an excellentgrounding rod. The tool is well grounded electrically to the water whichmay be otherwise poorly grounded to the Earth. This experimental setupwith the lowest water resistivity may simulate the actual tool workingenvironment in low resistivity formations. The truncated axial dimensionin the drillstring or Earth formation in the setup does not directlyimpact the experimental outcome because the differential measurementsbetween a pair of closely-spaced receivers is not sensitive toelectromagnetic properties of the regions truncated and altered in theexperimental setup. The truncated drill string and formation arereplaced by air above the tank and ground beneath the tank. Afunctioning tool is expected to produce results that match the modelprediction. This experiment is often conducted and its results are usedas a quality assurance point.

To experimentally obtain the tool response in a borehole in a formation,a thin-layer plastic tube may be used to simulate a borehole. The tubeis installed in the middle of a water tank vertically. A resistivitytool is placed in the middle of the tube separating the fluid inside thetube from the tank water. The fluid is acting as the drilling fluid(also called drilling mud) and the tank water is the formation. Thediameter of the tube may be chosen to match the diameter of a borehole.The salinity of the fluid inside the tube is varied to produce variousborehole mud resistivities used in drilling operations. Thisexperimental setup appears to accurately simulate the tool response in aborehole in a formation or a convenient method of testing the quality ofthe tool measurements in a borehole; however, this is not the case.

The plastic material of a tube is an electric insulator. The thininsulator cylinder does not significantly affect the propagation ofelectromagnetic wave generated by a tool with axial antenna in acylindrically symmetric environment. The insulation, however, destroysthe almost perfect direct grounding of the tool with the tank water.This problem can't simply be overcome by electrically attaching one endof an electric wire to the tool and the other end to a small conductingrod immersed in the tank. A small electric resistance may still existbetween the tool and the tank water. Also, this grounding problem can'tbe solved easily by grounding the water and the tool separately to Earthground. The electronics used to power the tool in a lab is oftengrounded to Earth ground already. The tank is often made of electricallyinsulating material such as fiber glass. The water in the tank is notdirectly grounded to the Earth without using a sizable metal structurewhich may interfere with tool's measurement. As a precision instrument,a resistivity tool is designed to be very sensitive to small signals. Ina low resistivity tank, a receiver voltage signal can be overwhelmed bynoises caused by the imperfect grounding of the tool to water in a tank.

For tool responses, modeling results are more accurate than laboratoryexperimental data in many situations. Experimental setup can introducenoises which do not exist in the downhole environment. Models, on theother hand, can match the true environment very well.

Tool response modeling may play a critical role in all stages of atool's life cycle. During the research and development phase, modelsimulations may be used to determine tool parameters such as frequency,antenna spacing, and measurement combinations. When a tool ismanufactured, modeling results are compared with data from tool tests todetermine the quality of a tool's performance. In tool's commercialoperations, modeling and its results are used for data conversion andinterpretation.

Due to complexity and intractability, some factors affecting antennagains are not included in the modeled tool response. The effect ofantenna gains on tool measurements are removed by using measurementcombinations such as compensated phase differences, for example. Sometools have antenna configurations and/or measurement combinations whichare not free of the effects of antenna gains. For those tools, theoutput-vs-temperature for each measurement is often established bysubjecting the tool to a range of temperatures. The effect oftemperature on each measurement is corrected based on the measurement'stemperature function. The temperature correction works well for antennasystems whose gains-vs-temperature is repeatable and the temperature inreal-time is accurately measured.

Even though a vast collection of borehole and formation structures canbe modeled, many details of a resistivity tool construct still cannot bemodeled on a computer. The structures of the antennas of a tool in atool model are much simpler than those of the actual hardware. Inaddition, the electric conductivities and magnetic permeabilities of thematerials used for antenna structures may not be precisely constant overthe temperature range of a tool. They are also slightly different fromtool to tool, and are not precisely known. The model simplification maybe necessary in order to compute tool responses on a computer. Themodeled tool is an approximation of the actual tool. Since modeled toolresponses are used in converting raw tool measurements to final tooldata, the discrepancy between a modeled tool response and that of theactual tool may cause errors in the measurement of formation properties.

In addition to ruggedness and reliability, two additional considerationsin designing the antennas of a LWD wave propagation resistivity tool areefficiencies and model-tractability.

LWD tools are generally cylindrical in shape so that they can beinstalled into and become part of the drill string. A cylindricalstructure that is the base for a LWD tool is called a sub. A directionparallel to the center line of the cylinder is the axial direction. Adirection perpendicular to the centerline is termed being cross-axial ortransverse.

FIG. 1 is a schematic side view of a steel sub 1 and antenna wire 4 ofan antenna section of one of the earliest resistivity tools in the priorart. FIG. 2 is a section view of the structure in FIG. 1 plus componentsof the antenna in a plane containing the cylindrical axis of the sub 1.Generally, the steel sub 1 is an antenna section. A circumferentialgroove 2 is cut from the steel sub 1. Some insulating material 3 (FIG. 2) is placed around a deepest surface 6 of the groove 2 to keep theantenna wire 4 some distance away from the deepest surface 6. Theantenna wire 4 is covered and protected by antenna cover 5 made ofnon-conducting material such as fiberglass.

In Towle, U.S. Pat. No. 5,138,263, hereinafter referred to as ‘Towle’,and incorporated by reference in its entirety, ferrite material withhigh magnetic permeability and negligible hysteresis is used as theinsulating material 3 in FIG. 2 . The ferrite dramatically improves theantenna efficiency.

To improve the mechanical reliability of the antenna section, severalslotted steel shells are used as the antenna cover 5 in FIG. 2 . Theshells cover the entire circumference and are clamped onto the sub bybolts. Slots of the steel shell are along the sub axial direction.

The use of ferrites and steel shells greatly improved the reliabilityand efficiency of the antenna design depicted in FIGS. 1 and 2 . Theimprovements, however, are not significant enough.

The steel shells of the antenna cover 5 can be damaged or the bolts cancome loose. An antenna section still needs to be repaired and rebuiltfrequently. The circumferential groove 2 in FIG. 1 weakens themechanical strength of the steel sub 1. The weakening makes it difficultto build resistivity tools with small cylindrical diameters.

Faraday's law of induction and Ohm's law on electric conduction causethe alternating electric current in the antenna wire 4 in FIG. 1 toinduce electric current underneath the antenna wire 4 on the surface 6of steel sub 1 in the deepest part of the circumferential groove 2. Assteel is highly conductive the current is in a thin layer at thesurface. The induced current generally flows in the opposite directionof the current in the antenna wire 4. Thus, the induced current may beviewed qualitatively as a line current underneath the antenna wire 4 onthe surface 6 of the deepest part of the circumferential groove 2, andmay be approximately equal in amplitude and opposite in sign to thecurrent in the antenna wire 4. Namely the induced current roughly formsan image of the current in the antenna wire 4. However, the total amountand distribution of the actual induced current depends on theconductivity of the steel, the gap between the antenna wire 4 and thesurface 6 of the deepest part of the circumferential groove 2 in FIGS. 1and 2 . Additionally, the shape of the antenna wire 4 may not beperfectly circular and/or concentric with the steel sub 1. The presenceof the ferrite between the antenna wire 4 and the surface of the steelsub 1 may also affect the induced current distribution.

For a transmitter antenna, the primary current in the antenna wire 4,the induced current in the steel sub 1, and aligned magnetic dipole inferrite material form the transmitting source of the antenna assembly.The total impedance of a transmitter antenna is affected by the presenceof the induced current in the steel sub 1. In particular the electricalresistance of the antenna assembly is a combination of the electricresistance in the antenna wire 4 and the resistance experienced by theinduced current in the steel sub 1. For a given power output by thetransmitter electronics circuitry, the electric current in the antennawire 4 of a transmitter antenna is determined by the total impedance ofthe antenna assembly. Similarly, the current measured by receiverelectronics in antenna wire 4 of a receiver antenna, is determined bythe electromagnetic field at the receiver location and the totalimpedance of the receiver antenna assembly.

The antennas are tuned to resonate at the operating frequency. The peakof the resonance is determined almost entirely by the electricresistance of the antenna assembly because the radiation loss is small.It is important that the electric resistance of an antenna assembly ismade as small as possible.

The steel sub 1 of an antenna section such as the one depicted in FIGS.1 and 2 is modeled as being a perfect cylinder without thecircumferential groove 2 cut for housing the antenna wire 4. Theschematic plot of a modeled antenna section is depicted in FIG. 3 .

FIG. 3 illustrates an antenna section 8 having a steel sub 9, an antennawire 10, and a gap 11. The gap 11 is positioned between the antenna wire10 and the surface of the steel sub 9. A transmitter serves as a perfectcurrent source in the model. A receiver serves as a perfect sensor ofvoltage or electromagnetic force. Both the steel sub 9 and current ofthe antenna wire 10 may be assumed to be perfectly circular and areconcentric. This model is termed Sleek-Collar Current-Loop (SCCL) model.

The simplification of the antenna section 8 in the model makes itpossible to compute the tool response analytically in various boreholeand formation environments. Because the wave length of theelectromagnetic signal used by a resistivity tool is much larger thanthe dimension of the antenna section 8, the simplification used in themodel is justified for differential measurements between two receivers.However the justification is based on the antenna wire 10 beingperfectly circular and concentric with the steel sub 9. In reality, theshape of the antenna wire 10 may be different from that of the model.The distribution of the induced current in the steel sub 9 may bedifferent from the model prediction. This is a source of error.

The tool response is sensitive to the conductivity of the steel sub 9even if the antenna wires 10 are perfectly circular and concentric. Thesize of the gap 11 between the antenna wire 10 and the surface of thesteel sub 9 underneath may also affect the tool response. So theconductivity of the steel and the gap must be accounted for precisely inthe model used to compute the tool response. Thus inaccuracies inmanufacturing processes and inconsistencies in materials causeresistivity measurement error.

The type of antenna depicted in FIG. 1 has at least three major shortcomings. First, the steel sub 1 (antenna section) may be easily damaged.Second, the induced current in the steel sub 1 experiences a higherelectric resistance than that of the antenna wire 4 made of copper,limiting the antenna efficiency. Third, the distribution of the inducedcurrent is sensitive to the details of antenna structure and theproperties of the materials used in the antenna section. Thedistribution is often unknown and is not correctly-accounted for in amodel, potentially causing resistivity measurement errors.

The antenna reliability was greatly improved in a design by Wisler etal., U.S. Pat. No. 5,530,358, hereinafter referred to as ‘Wislerdesign’, or ‘Wisler antenna’), and incorporated by reference in itsentirety.

FIG. 4 is a schematic and non-proportional side view of an antennasection 13 using the design by Wisler et al. The antenna section 13includes a steel structure 14. Slots are cut in parallel to the axis ofthe tool cylinder and are approximately evenly distributedcircumferentially. Nine slots are viewable in FIG. 4 . Only one slot isshown with label 15 in FIG. 4 for simplicity. “A slot 15” or “a slot”means any of the nine slots shown and the slots not shown. “Slots 15”refers to the collection of all the slots. Wire holes are pathways inthe steel structure 14 between slots 15. The label 31 refers to a singlesection of wire hole connecting two adjacent slots. For simplicity onlyone wire hole is labeled 31 in FIG. 4 . But “a wire hole 31” or “a wirehole” is used to refer to any of the wire holes. “Wire holes 31” refersto the collection of all the slots. Slots 15 and wire holes 31 form acircumferential pathway for antenna wire (not shown).

FIG. 5 is a cross-sectional view of the antenna section 13 in a planethat is perpendicular to the cylindrical axis of the antenna section 13and is at the antenna wire 32 in a Wisler antenna. The antenna wire 32in FIG. 5 is illustrated as a dashed line. Wire holes 31 are positionedat a distance away from the surface of the sub. The insulating material33 may include a magnetic ferrite rod positioned in the section (e.g.,bottom section) of a slot 15 under the antenna wire 32. The insulatingmaterial 33 (e.g., a ferrite rod) may be made of high magneticpermeability material without hysteresis. Even though only one label 33is shown in FIG. 5 for simplicity the label applies to all 16 pieces ofthe insulating material. Filler material 49 that is non-conductive andnon-magnetic is used to fill the space in the slots 15 above the antennawire 32 for protection of the antenna. A wire passageway 65 providesaccess for the antenna wire 32 to electronic circuitry. Here, an objectA being above or over an object B in the slot 15 means that A isradially closer to the surface of a sub than B. Conversely object Abeing under or beneath object B indicates A is radially closer to thecenter line of a sub than B.

FIG. 6 is an expanded view of antenna wire 32 and ferrite rods 33. Thesteel structure and other components in the antenna structure are notshown in FIG. 6 . Wire segments 66 and 67 connect the antenna wire 32 toand from an electronic circuitry 68. The antenna wire 32 and wiresegments 66 and 67 may be made of a single continuous wire. The wiresegments 66 and 67 may be twisted. The currents in wire segments 66 and67 have substantially the same amplitude and are opposite in direction.The wire segments 66 and 67 together may not materially contribute tothe receiving or transmitting function of the antenna structure,especially when well-twisted.

Referring to FIG. 5 , for a transmitter antenna, the current in antennawire 32 forms a current loop. The current induces currents at the bottomof the slots under ferrite rods, walls of wire pathway 31, side walls ofslots, and surface of the antenna sub. The total strength of the inducedcurrent in the azimuthal direction is approximately equal to that of theantenna wire 32 as in the case for an antenna depicted in FIGS. 1 and 2. Even though the main antenna transmitting power comes from the ferriterods, the induced current is still a factor. The electric resistanceencountered by the induced current is also important in limiting theheight of antenna resonance.

The Wisler design is one of the strongest antenna structures, and almosteliminates the need for mechanical maintenance and repair of the antennasections. Mechanically the antenna structure is easy to make. There isstill substantial induced current in the steel structure around theantenna wire. The electric resistance in steel still limits the heightof the resonance of the tuned antenna assembly. More importantly thedistribution of the induced current is still not explicitly accountedfor in a model. The distribution may vary from antenna to antenna andfrom tool to tool due to the variation in steel conductivity and thedetails of the antenna construct. Usually the model used for toolresponse in a borehole environment, data processing and loginterpretation is the sleek-collar loop current model (SCLC) depicted inFIG. 3 .

In Wu, (U.S. Pat. Nos. 5,331,331 and 5,491,448, both herein incorporatedby reference in their entirety), each antenna is made of one or moremagnetic dipoles (Point dipole antenna, or Wu antenna). The dipoles areplaced in pockets cut on the surface of steel sub. Each magnetic dipoleconsists of or can be thought of as an electric current loop. Inparticular, a dipole is made of a current wire wrapped around a ferriterod with high magnetic permeability. The current loop in this case ismuch smaller than the diameter of the steel sub and the wave length ofthe electromagnetic wave used in resistivity tools. The dipole inducedcurrent in the steel sub is much smaller than that of thecircumferential current loop around the steel sub as in the Wislerdesign or the groove structure depicted in FIG. 1 if the currents in thedipole and in the circumferential loop are the same. Smaller inducedcurrent means that the conductivity of the steel sub plays a smallerrole in antenna efficiency. In turn, proper modeling of the detaileddistribution of the induced current becomes less important. A simplifiedstructure for antennas can be used to approximate the real antenna in amodel so that model computations can be carried out. The axial antennasection of a model used for tool response in homogenous media or aborehole environment for an antenna consisting of three point dipoles isdepicted in FIG. 7 .

In FIG. 7 , an axial antenna section 69 includes a steel sub 70 thatextends in both directions with constant outside-diameter. Magneticpoint dipoles 71, 72 and 73 are in the axial direction of the steel sub70. There exists a distance d between the surface of the steel sub 70and the magnetic point dipoles 71, 72 and 73. This antenna is termedSleek-Collar Point-Dipole (SCPD) model. Point-dipole antennas innon-axial directions are also modeled by SCPD. For aforementionedreasons, SCPD models tool response with point-dipole antennas muchbetter than SCLC does with Wisler design.

There exists a need within the art for an antenna for a LWD tool withefficiency and model tractability, while ensuring mechanical structureintegrity, manufacturability and/or zero-maintenance.

BRIEF DESCRIPTION OF THE DRAWINGS

Like reference numerals in the figures represent and refer to the sameor similar element or function. Embodiments of the present disclosuremay be better understood when consideration is given to the followingdetailed description thereof. Such description makes reference to theannexed pictorial illustrations, schematics, graphs, drawings, andappendices. In the drawings:

FIG. 1 is a schematic side view of a prior art steel structure andantenna wire of an antenna section.

FIG. 2 is the section view of the structure in FIG. 1 having componentsof the antenna in a plane containing a cylindrical axis of a sub.

FIG. 3 is a schematic view of a model used for antennas depicted inFIGS. 1 and 2 .

FIG. 4 is a schematic and non-proportional side view of an antennasection in a prior art design by Wisler et al.

FIG. 5 is a cross-sectional view of the antenna structure at the antennawire.

FIG. 6 is a schematic expanded view of antenna wire and ferrite rods ofFIG. 5 .

FIG. 7 is an axial antenna section of a prior art model used forpoint-dipole.

FIG. 8 is a schematic cross-sectional view of an antenna wire section ofan antenna using an embodiment of the current disclosure.

FIG. 9 is an expanded view of antenna wire and ferrite rods of FIG. 8 .

FIG. 10 is a schematic cross-sectional view of the net current of anantenna wire section of an antenna with an embodiment of the currentdisclosure.

FIG. 11 is a schematic side view of the steel structure of a cross-axialantenna section.

FIG. 12 is a schematic view of the antenna section illustrated in FIG.11 rotated 90 degrees about its cylindrical axis.

FIG. 13 shows a section view of a prior-art cross-axial antenna in aplane containing the tool major axis and being perpendicular to the axisof the cross-axial antenna.

FIG. 14 shows a section view of a cross-axial antenna in a planecontaining the tool major axis and being perpendicular to the axis ofthe cross-axial antenna.

FIG. 15 shows a section view of the net current in antenna wires in across-axial antenna in a plane containing the tool major axis and beingperpendicular to the axis of the cross-axial antenna.

FIG. 16 is a schematic diagram of one half of an antenna wire in a priorart axial and cross-axial combination antenna.

FIG. 17 is a schematic diagram of one half of an antenna wire in anaxial-cross-axial combination antenna.

FIG. 18 is a schematic diagram of two halves of an antenna wire in anaxial-cross-axial combination antenna.

FIG. 19 is a diagram of the antenna wire in a cross-axial antenna.

FIG. 20 is a side view of the bare steel structure of a cross-axialantenna section.

FIG. 21 is a cross-sectional view of a quadrupole antenna at the antennawire section.

FIG. 22 is an antenna wire diagram of a quadrupole antenna.

FIG. 23 is a schematic flow diagram of a transceiver electronics systemin accordance with the present disclosure.

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS

Generally, multiple slots are cut around the surface of an antennasection. For axial antennas, the slots are in the direction of acylindrical axis of a tool and are distributed circumferentially.Beneath a sub-surface, wire holes perpendicular to the slots are made toconnect the slots, forming a circumferential wire passageway. Highlymagnetically-permeable ferrite rods are positioned in the slots. Anantenna wire is positioned in a first direction around in a wire pathabove the ferrite rods. The antenna wire is then positioned in a seconddirection in an opposite direction of the first position such that theantenna wire is underneath the ferrite rods. Net current in a wire holeconnecting two adjacent slots is zero. The net current around eachferrite rod forms a closed loop. Each ferrite rod may act as a pointdipole. A group of point dipoles forms an antenna. The slot structuremakes the antenna structure durable. Electric current in and around wireholes and slots induced by antenna current is much smaller than that ofany prior art antenna structure. The antenna efficiency is improved. Theantenna response is well tracked by a model with point-dipole antennas.An antenna in a non-axial direction can be made by a group of slots cuton the sub surface in a pre-designed direction. Wire holes, ferriterods, and antenna wire are arranged in a way similar to that of axialantenna.

Before explaining at least one embodiment of the present disclosure indetail, it is to be understood that embodiments of the presentdisclosure are not limited in their application to the details ofconstruction and the arrangement of the components or steps ormethodologies set forth in the following description or illustrated inthe drawings. The inventive concepts in the present disclosure arecapable of other embodiments or of being practiced or carried out invarious ways. Also, it is to be understood that the phraseology andterminology employed herein is for the purpose of description and shouldnot be regarded as limiting.

In this detailed description of embodiments of the inventive concepts,numerous specific details are set forth in order to provide a morethorough understanding of the inventive concepts. However, it will beapparent to one of ordinary skill in the art that the inventive conceptsdisclosed and claimed herein may be practiced without these specificdetails. In other instances, well-known features have not been describedin detail to avoid unnecessarily complicating the instant disclosure.

As used herein, language such as “including,” “comprising,” “having,”“containing,” or “involving,” and variations thereof, is intended to bebroad and encompass the subject matter listed thereafter, equivalents,and additional subject matter not recited or inherently present therein.

Unless expressly stated to the contrary, “or” refers to an inclusive orand not to an exclusive or. For example, a condition A or B is satisfiedby anyone of the following: A is true (or present) and B is false (ornot present), A is false (or not present) and B is true (or present),and both A and B are true (or present).

In addition, use of the “a” or “an” are employed to describe elementsand components of the embodiments herein. This is done merely forconvenience and to give a general sense of the inventive concepts. Thisdescription should be read to include one or at least one and thesingular also includes the plural unless it is obvious that it is meantotherwise.

Throughout this disclosure and the claims, the terms “about,”“approximately,” and “substantially” are intended to signify that theitem being qualified is not limited to the exact value specified, butincludes slight variations or deviations therefrom, caused by measuringerror, manufacturing tolerances, stress exerted on various parts, wearand tear, or combinations thereof, for example.

The use of the term “at least one” will be understood to include one andany quantity more than one, including but not limited to each of, 2, 3,4, 5, 10, 15, 20, 30, 40, 50, 100, and all integers therebetween. Theterm “at least one” may extend up to 100 or 1000 or more, depending onthe term to which it is attached; in addition, the quantities of100/1000 are not to be considered limiting, as higher limits may alsoproduce satisfactory results. Singular terms shall include pluralitiesand plural terms shall include the singular unless indicated otherwise.

The term “or combinations thereof” as used herein refers to allpermutations and/or combinations of the listed items preceding the term.For example, “A, B, C, or combinations thereof” is intended to includeat least one of: A, B, C, AB, AC, BC, or ABC, and if order is importantin a particular context, also BA, CA, CB, CBA, BCA, ACB, BAC, or CAB.Continuing with this example, expressly included are combinations thatcontain repeats of one or more item or term, such as BB, AAA, AAB, BBC,AAABCCCC, CBBAAA, CABABB, and so forth. The skilled artisan willunderstand that typically there is no limit on the number of items orterms in any combination, unless otherwise apparent from the context.

Circuitry, as used herein, could be analog and/or digital components, orone or more suitably programmed microprocessors and associated hardwareand software, or hardwired logic. Also, certain portions of theimplementations may be described as “components” that perform one ormore functions. The term “component,” may include hardware, such as aprocessor, an application specific integrated circuit (ASIC), or a fieldprogrammable gate array (FPGA), or a combination of hardware andsoftware. Software includes one or more computer executable instructionsthat when executed by one or more component cause the component toperform a specified function. It should be understood that thealgorithms described herein are stored on one or more non-transitorymemory. Exemplary non-transitory memory includes random access memory,read only memory, flash memory or the like. Such non-transitory memorycan be electrically based or optically based.

As used herein any reference to “one embodiment” or “an embodiment”means that a particular element, feature, structure, or characteristicdescribed in the embodiment is included in at least one embodiment. Theappearances of the phrase “in one embodiment” in various places in thespecification are not necessarily referring to the same embodiment,although the inventive concepts disclosed herein are intended toencompass all combinations and permutations including one or morefeatures of the embodiments described.

In the present disclosure, LWD may mean both FEMWD and LWD.

A resistivity tool within the present disclosure refers to a LWD wavepropagation resistivity tool exclusively unless specified otherwise.

Referring to FIG. 8 , illustrated there in is a schematiccross-sectional view of an exemplary embodiment of antenna wire 75 of anantenna section in accordance with the present disclosure. The view isin a plane that is perpendicular to the cylindrical axis of the antennasection and the plane is at the location of the antenna wire 75. Thereare sixteen slots in FIG. 8 . Only one is labeled explicitly 15 a forsimplicity. “A slot 15 a” may refer to any one of the sixteen. Similarlyone label 33 a and one label 31 a are explicitly shown in FIG. 8 for anyof the sixteen ferrite rods and any of the sixteen wire hole sections,respectively. The antenna wire 75 goes above every ferrite rod 33 a.This section of antenna wire 75 is similar to antenna wire 32illustrated in FIG. 5 . The antenna wire 75 turns around and goesunderneath every ferrite rod 33 a in the opposite direction. Two wiresegments 76 and 77 of the antenna wire 75 are in a wire hole 31 abetween two adjacent slots 15 a. Even though a pair of wire segments inonly one wire hole is labeled 76 and 77, respectively in FIG. 8 forsimplicity every pair of wire segments in every one of the 16 wire holesare referred to as 76 and 77. The currents in a pair of wire segments 76and 77 are the same in amplitude but opposite in direction, for example.In should be noted, the wire segments 76 and 77 may be closer andtightly bound together within the wire hole 31 than what is illustratedin FIG. 8 . The net current in a wire hole 31 a connecting two adjacentslots 15 a is zero. During the manufacturing process, one portion of theantenna wire 75 (e.g., the bottom portion) may be laid first threadingthe slots 15 a and wire holes 31 a. Then, the ferrite rod 33 a may beplaced in the slot 15 a on top of the sections of wire 75 already in theslot 15 a. Finally, the antenna wire 75 turns around and goes aroundthrough the wire hole 31 a and on top the ferrite rod 33 a. The antennawire 75 can be made of a single continuous wire section or multiple wiresections electrically connected together in sequence.

The expanded views of the antenna wire 75 and ferrite rods 33 a of FIG.8 are schematically shown in FIG. 9 . Referring to FIGS. 8 and 9 , wiresegments 76 and 77 are positioned in a section of the wire hole 31 abetween two adjacent slots 15 a with ferrite rods 33 a. It should benoted that the wire segments 76 and 77 may be more tightly positionedthan what is illustrated within FIGS. 8 and 9 . For example, in someembodiments, outer claddings of the wire insulation of the two wiresegments 76 and 77 may touch each other. The antenna wire 75 may also bepositioned closer to the ferrite rods 33 a than what is illustrated inFIGS. 8 and 9 .

FIG. 10 is a cross-sectional view of net current 79 of the antenna wire75 illustrated in FIG. 8 . The wire segments 76 and 77 in a wire hole 31a carry equal amount of currents in opposite directions. The net current79 in the wire segments 76 and 77 in any wire hole 31 a is zero. The netcurrent 79 around each ferrite rod 33 a forms a closed loop encirclingthe ferrite rod 33 a. Ferrite rod 33 a then becomes a point-dipole. Aseparation between the wire segments 76 and 77 in the wire hole 31 acauses the formation of a closed current loop 80 in the wire hole 31 aas shown in FIG. 10 . The separation, however, is limited by thediameter of the wire hole 31 a. Therefore, the encircled area by theclosed current loop 80 means the net current 79 is small, such that themagnetic dipole moment associated with the closed current loop 80 isnegligible relative to the dipole moment of the ferrite rod 33 a with ahigh magnetic permeability. It should be noted that the closed currentloop 80 around the ferrite rod 33 a does not have to be tightly wrappedaround the ferrite rod 33 a as illustrated in FIG. 10 . The closedcurrent loop 79 can loosely encircle the ferrite rod 33 a. Magneticdipole moment of the ferrite rod 33 a is insensitive to how tight theclosed current loop 79 is about the ferrite rod 33 a. As such, there isno need to impose restrictions on how the wire segments 76 and 77 arepositioned about the ferrite rod 33 a during a manufacturing process.

The point-dipoles may point in the same direction as shown in FIGS. 8, 9, and 10, acting coherently. The collection of all the magnetic pointdipoles forms a composite magnetic dipole in the axial direction. Thiscomposite dipole is an axial antenna. Hereafter, parallel slot-baseddipoles are called in phase when pointing at the same direction amongthemselves. Two groups of parallel dipoles are completely out of phasewhen at any moment the direction of a dipole from one group is oppositeto the direction of a dipole from the other group. For a group includingsubgroups of parallel dipoles at different orientations, the group is inphase if each subgroup at an orientation is in phase.

Wu antenna includes designs for non-axial antenna made of a collectionof coherent point-dipoles pointing in a desired direction. Wisler etal., (U.S. Pat. No. 9,885,800, herein referred to as Wisler 2006, andincorporated by reference in its entirety), teaches the designs ofcross-axial and other non-axial antennas with slot and slot-likestructures (Wisler 2006).

FIG. 11 is a prior art cross-axial antenna section 89 including a steelstructure 91 as described by Wisler 2006. The coordinate system 94 showsthat the Z-axis is a center axis of the steel structure 91. The Y-axisof the coordinate system 94 is directed outward. A plurality of holes 92on the steel structure are positioned in the X-direction of thecoordinate system 94. The plurality of holes 92 are connected by slotopenings 93 on the steel structure. Generally, the slot opening 93 mustbe narrower than the opening of a typical axial slot such thatnon-conductive material filling the slot opening 93 is not damaged bythe abrasive drilling mud while the tool is rotating. The hole 92 iscreated by drilling through on the sub surface of the steel structure 91in the X-direction. The diameter of each hole 92 is larger than thewidth of the surface opening of the adjacent slot opening 93 so that asizable ferrite rod can be placed in the hole 92. The dipole moment of aferrite rod is proportional to its cross sectional area. The dipolemoment of the ferrite rod is insensitive to the cross-sectional shape.The use of ferrite rods with rectangular and round cross-sections foraxial and cross-axial antennas, respective, is simply due to how theslot(s) 15 and hole(s) 92 are machined. Even though the geometries of anaxial slot 15 in FIG. 4, 5 or 15 a in FIGS. 8, 10 and a combination ofthe hole 92 and the slot opening 93 are different, each may function asa slot. Hereafter, a combination of one hole 92 and one adjacent slotopening 93 is referred to as a slot.

The actual width of the slot opening 93 can be made smaller than what isshown in the schematic view of FIG. 11 . The slot opening 93 can be cutwith the smallest mechanic knife in the machining process, for example.Because of the low frequency (<=10 MHz) used in LWD resistivity tools,the capacitive impedance of the slot opening 93 is very large. Forexample, there is no closed loop for induced current to kill the ferritesignal.

FIG. 12 is another side view of the prior art steel structure 91illustrated in FIG. 11 . In this view, the steel structure 91 is rotated90 degrees about its cylindrical axis from the position in thecross-axial antenna section 89 of FIG. 11 . The X-axis of the coordinatesystem 94 is pointing into the paper.

FIG. 13 illustrates an expanded view 95 on a section of the antennasection 89 of FIG. 12 . The coordinate system 100 is at the X=0 plane inthe coordinate system 94 in FIGS. 11 and 12 . The antenna 95 includesferrite rods 96, wire holes 98 and antenna wire 99. Non-conductive andnon-magnetic material 97 is positioned within slot openings 93. Similarto the axial antenna of Wisler design, electric current is induced inwalls of the steel structure 91 around the ferrite rod 96 and in thewire hole 98. As in the case of axial antennas, the dominanttransmitting or receiving power comes from the ferrite rods 96. Theinduced current still plays a role in the transmission or receivingfunction of the antenna 95. The steel conductivity plays a big role inimpedance of the antenna 95. The details of geometry of the ferrite rods96 and wire placement in the wire hole 98 influence the distribution ofthe induced current and impedance of the antenna 95. The induced currentis thus not well tracked by models used to compute tool response invarious borehole and formation environments.

FIG. 14 is an exemplary embodiment of a cross-axial antenna 101. Anantenna wire 102 is positioned about ferrite rods 96 a in oppositedirections. Two wire segments 76 a and 77 a in a wire hole 98 a connecttwo adjacent slots 93 a. Currents in the two wire segments 76 a and 77 aare substantially equal in magnitude and opposite in directions. Netcurrent in a wire hole 98 a between slots 93 a is zero.

FIG. 15 is a schematic view of the cross-axial antenna 101 illustratingnet current 104. Net current 104 about each ferrite rod 96 a forms aclosed loop around the ferrite rod 96 a. Each ferrite rod 96 a becomes apoint dipole. As such, a collection of point dipoles forms a cross-axialantenna.

FIG. 16 is a schematic antenna wire diagram for one half of the X-Zantenna combo 150 in Wisler 2006. The antenna wire 111 consists of twohalf circles and two straight lines. A tuning circuit 112 is connectedto a Trans-Receiver Circuit (not shown) via a connector 113. Ferriterods (not shown) are placed in slots perpendicular to the antenna wire111 in both circular and straight sections. Every ferrite rod is inbetween the segment of the antenna wire 111 in the slot (not shown) andthe steel bottom of the slot. The steel structure, ferrite rods,non-conducting material filling the slot between the antenna wire 111and the surface of the antenna sub are not shown so that the generalwire route can be clearly depicted. The diagram of the antenna wire ofthe other half of the X-Z antenna combo is very similar. The maintransmitting or receiving power comes from the ferrite rods. Wiresegments not in slots as well as the steel structure still affectantenna power. The wires from the two halves are connected to the singleTrans-receiver Circuit. The Trans-Receiver Circuit operates the twohalves simultaneously in a desired mode.

FIG. 17 is a schematic wiring diagram of one half of an X-Z antennacombo 152. The antenna wire 114 goes through a route below ferrite rods(not shown) and then turns around to go through the route again in anopposite direction above the ferrite rods. The net current is zeroeverywhere except in any slot (not shown) where a ferrite rod issandwiched between the two opposite wire segments in a slot. The netcurrent around a ferrite rod forms a closed loop. Only ferrite rods andimmediate surroundings perform the transmitting or receiving function ofthe antenna. Wire-hole sections connecting slot-to-slot andslot-to-electronics do not participate in transmitting or receivingfunction directly. The SCPD model, not having wire hole sections,simulates this antenna structure.

The tuning circuit 112 a illustrated in FIG. 17 may be similar to thetuning circuit 112 in FIG. 16 . In some embodiments, the tuning circuit112 a may include different electronic components such as capacitors asantenna wire 111 in FIG. 16 and antenna wire 114 in FIG. 17 may havedifferent inductances.

In some embodiments the antenna mechanical structures and structures forhousing antenna tuning circuits and transceiver circuit as well as wirepathways between different locations may be very similar to those ofprior art. Existing tools may be upgraded to include an embodiment ofthe current invention with no or small modifications in mechanicalstructures.

The structure that includes slots and wire holes for both halves of theX-Z antenna combo 152 is hereafter termed an X-Z steerable antennastructure or simply a steerable antenna structure. The slot and wirehole locations and orientations are also hereafter referred to being ina steerable antenna pattern. Hereafter, the wire route in FIG. 17 , anda similar route for the other half of the X-Z antenna combo 152, arereferred to as being steerable antenna routes.

FIG. 18 depicts the two antenna wires 114 and 114 a for both halves ofan X-Z steerable antenna 154 in steerable routes. The directions of Xand Z are defined in coordinate system 116. The Z-axis coincides with acylindrical axis of the segment of the X-Z steerable antenna 154. Thecross-axial slots (not shown) are in the X-direction. Generally, theroute of the second antenna wire 114 a is the first wire 114 rotatedabout the tool cylindrical axis by 180 degrees except the locationswhere the antenna wires 114 and 114 a connect to tuning circuit 112 and112 a. Both antenna wires 114 and 114 a connect to the trans-receivercircuit 140 via connectors 113 and 113 a, respectively. The cross-axialferrite rods (not shown) positioned in the straight sections in FIG. 18are powered (if the X-Z steerable antenna 154 is a transmitter) orsensed (if the X-Z steerable antenna 154 is a receiver) by both antennawires 114 and 114 a. The net current around a cross-axial ferrite rodforms two closed loops from the two antenna wires 114 and 114 a. Thereare four wire segments in each wire hole connecting two adjacentcross-axial ferrite rods. Two of the wire segments come from the firstantenna wire 114 and the other two segments come from the second antennawire 114 a. The net current in the wire hole is zero. Any axial ferriterod in a circular section is powered or sensed by one wire. The netcurrent in an axial ferrite rod forms one closed loop. One half of theaxial ferrite rods on one complete circular section are powered orsensed by one wire and the other half by the other wire.

As a transmitter the X-Z steerable antenna 154 can be made to be a pureaxial dipole or a pure cross-axial dipole or a slant dipole pointing ina direction between Z and X. If the current amplitudes are the same inthe two antenna wires 114 and 114 a (zero relative amplitude, or unitamplitude ratio) and the phases are such that the two closed net currentloops around a cross-axial ferrite rod are exactly 180 degrees out ofphase, then the total net current around a cross-axial ferrite rod iszero. The net currents on all the axial ferrite rods are the same andare in phase. The transmitter is a pure axial magnetic dipole antenna.If the two closed net current loops on a cross-axial ferrite rod are inphase, then the net current loops around axial ferrite rods powered bythe first antenna wire 114 are 180 degrees out of phase with those ofthe second antenna wire 114 a. One half of the axial ferrite rods on ahalf circle are 180 degrees out of phase with the other half. If theamplitude ratio between the two wire currents is one, then the net axialdipole moment for each circle is zero. The axial ferrite rods on onecircle forms a quadrupole. A second quadrupole is formed from the othercircle of axial ferrite rods. The two quadrupoles are completely out ofphase. The total quadrupole moment is also zero. The two quadrupoles areseparated by the distance between the two circles. There is a smalloctupole that has a negligible effect on the antenna. The transmitterbehaves as a cross-axial magnetic dipole antenna.

The phase of a transmitting ferrite rod without hysteresis is that ofthe wire current. The relative phase between the magnetic dipolecomponents excited by the two wire currents is that of the two wirecurrents. The collective magnetic dipole in a cross-axial direction inthe X-Z steerable antenna 154 depicted in FIG. 18 is:M _(x) =CI ₁[sin(ωt)+B sin(ωt+φ)]  (EQ. 1)wherein x is the cross-axial axis defined by the cross-axial slots inthe X-Z steerable antenna 154, I₁ is the current in wire 114, M_(x) isthe magnetic dipole moment in the x direction, product CI₁ is theamplitude of the total magnetic dipole moment in the x-direction poweredby the current in antenna wire 114, B is the amplitude ratio of currentin wire 114 a over current in wire 114, ω is the current frequency, sin() is the sine function, and φ is the relative phase between the twocurrents.

Each cross-axial ferrite rod is powered by both a first current and asecond current. The first term on the right hand side of EQ. 1 is themagnetic dipole generated by the first current. The second is by thesecond current. Without a loss of generality, the phase of thecollective cross-axial dipole is defined as being relative to that ofthe first current. As such, the phase of the first term is zero and thephase for the second term is the relative phase between the two terms.

EQ. 1 can be rewritten as:M _(x) =CI ₁√{square root over (1+B ²+2B cos(φ))}sin{ωt+A TAN 2[Bsin(φ),1+B cos(φ)]}  (EQ. 2)wherein cos( ) is the cosine function and A TAN 2[ ] is the inversetangent function with two arguments. The amplitude and phase of thecollective cross-axial dipole are CI₁√{square root over (1+B²+2Bcos(φ))} and A TAN 2[B sin(φ), 1+B cos(φ)], respectively.

The collective magnetic moment in an axial direction is:M _(z) =AI ₁[sin(ωt)−B sin(ωt+φ)]  (EQ.3)wherein z is the axial axis defined by the axial slots in the X-Zsteerable antenna 154, M_(z) is the total magnetic dipole moment in thez direction, AI₁ is the amplitude of the total magnetic dipole moment inthe z-direction powered by the first current.

Each axial ferrite rod is powered by either the first current or thesecond current, but not by both. The first term on the right hand sideof EQ. 3 is the total axial magnetic moment powered by the firstcurrent. The second is by the second current. The minus sign between thetwo terms is the result of the two cross-axial dipole components poweredby the two currents being additive, the two axial dipole componentspowered by the two currents are subtractive, and vice versa. Thisproperty is determined by the steerable wire routes by design.Therefore, the two signs between the two terms in EQS. 1 and 3 areopposite. Which of the two signs is plus is a choice on how the relativephase between the two currents is defined. If the relative phase betweenthe two currents is defined to be φ+180 instead of φ, then the two signsin EQS. 1 and 3 are reversed. Both choices on relative phase are equallyvalid. Antenna property and behavior do not depend on which choice isused in the equations. Hereinafter, the relative phase between the twocurrents is the φ used in EQS. 1 and 3. The phase of the collectiveaxial dipole is also defined as being relative to that of the firstcurrent.

EQ. 3 can be rewritten as:M _(z) =AI ₁√{square root over (1+B ²−2B cos(φ))}sin{ωt+A TAN 2[−Bsin(φ),1−B cos(φ)]}  (EQ. 4)The amplitude and phase of the collective axial dipole areAI_(n)√{square root over (1+B²−2B cos(φ))} and A TAN 2[−B sin(φ), 1−Bcos(φ)] respectively. The relative phase between the collectivecross-axial dipole and the collective axial dipole is A TAN 2[B sin(φ),1+B cos(φ)]−A TAN 2[−B sin(φ), 1−B cos(φ)].

The total collective dipole vector is a vector sum of M_(x) and M_(z) inorder to have a magnetic dipole in a constant direction (a lineardipole), the relative phase between the cross-axial component M_(z) andaxial component M_(z) must be zero or a multiple of 180 degrees. Assuch:A TAN 2[B sin(φ),1+B cos(φ)]−A TAN 2[−B sin(φ),1−B cos(φ)]=nπ  (EQ. 5)wherein n=0, ±1 and π is the Archimedes' constant (the ratio of acircle's circumference to its diameter).

EQ. 5 is applicable only when neither M_(x) nor M_(z) has a zeroamplitude. When the amplitude of M_(z) is zero the resulting collectivedipole is a linear dipole in a cross-axial direction regardless of itsphase. Similarly, when the amplitude of M_(x) is zero the resultingcollective dipole is a linear dipole in an axial direction regardless ofits phase. It can be proven that the necessary and sufficient conditionfor either M_(x) or M_(z) to have a zero amplitude is (B=1 andsin(φ)=0). The (B=1 and φ=0 degrees) condition results in thetransmitter being a cross-axial dipole with zero axial dipole moment.The (B=1 and φ=180 degrees) condition results in the transmitter beingan axial dipole with zero cross-axial dipole moment.

If B=1 and sin(φ)≠0, then the relative phase between the two dipolecomponents is 90 or −90 degrees. EQ. 5 is thus violated. Therefore, the(B=1 and sin(φ)≠0) condition leads to the transmitter being anonlinearly-polarized dipole. The resulting transmitter is anelliptically polarized magnetic dipole. The eccentricity of the ellipseis a function of the relative phase φ between the first current and thesecond current. When

$\varphi = {{\pm 2}{{ATAN}\left( \sqrt{\frac{C}{A}} \right)}}$where A TAN( ) is the inverse tangent function, the ellipse becomes acircle. The transmitter becomes a circularly polarized magnetic dipoleantenna. When sin(φ) is zero. the ellipse degenerates into a line. Theresulting transmitter is a linearly polarized dipole. For B=1 thetransmitter can be made into an elliptically polarized magnetic dipolewhen sin(φ)≠0, or a linearly polarized magnetic dipole in a cross-axialdirection when φ=0, or a linearly-polarized magnetic dipole in an axialdirection when φ=180 degrees. To make a steerable transmitter into alinearly polarized magnetic dipole antenna in a direction between theaxial and cross-axial axes the two wire currents must be different.

For B #1 EQ. 5 gives us

$\begin{matrix}\begin{matrix}{\frac{2B\sin(\phi)}{1 - B^{2}} = 0} & {{{for}B} \neq 1.}\end{matrix} & \left( {{EQ}.6} \right)\end{matrix}$

There are four solutions to EQ.6: B=0; B=∞; φ=0; and φ=180 degrees. Bbeing zero means that the second current is zero and the first currentis non-zero. The resulting transmitter is a slanted linear dipole. Theslant angle of the dipole relative to the axial axis is

${{ATAN}\left( \frac{C}{A} \right)}.$B being infinite indicates that the first current is zero and the secondcurrent is non-zero. The resulting transmitter is a slanted lineardipole with a slant angle of

$\pi - {{{ATAN}\left( \frac{C}{A} \right)}.}$A linear dipole with a slant angle at

$\pi - {{ATAN}\left( \frac{C}{A} \right)}$in the X-Z plane is a linear dipole at

$- {{ATAN}\left( \frac{C}{A} \right)}$with a 180 degree phase difference. The route of wire 114 and route ofwire 114 a in the routes of the steerable antenna 154 are identicalexcept that they are 180 degrees apart azimuthally about the antennacylindrical axis. The azimuthal angle of a tool about its cylindricalaxis (drill string axis) is termed tool face. Rotating the antennacylinder by 180 degrees in tool face, the two wire routes switchpositions. Because the axial slot structure and ferrite rods areidentical among themselves, the amplitude ratio between the totalcross-axial and axial dipoles when only current 2 is non-zero (B=00) isthe same as that when only current 1 is non-zero (B=0). The absolutevalues of the slant angles in those two cases are the same. The onlydifference between the two cases is that the two slanted dipoles are 180degrees apart both in tool face and in dipole phase. The ratio

$\frac{C}{A}$is independent of the amplitude of the wire current. It is determined bythe steerable antenna structure.

When φ=0 the X-Z steerable antenna 154 becomes a linearly-polarizedmagnetic dipole with a slant angle

$\theta_{s} = {{ACOS}\left\lbrack \frac{A\left( {1 - B} \right)}{\sqrt{{C^{2}\left( {1 + B} \right)}^{2} + {A^{2}\left( {1 - B} \right)}^{2}}} \right\rbrack}$from the cylindrical axis of the steerable antenna 154, wherein A COS( )is the inverse of cosine function. The slant angle is a function of B. Bcan be chosen to be a value in the domain [0, +∞). The range of θ_(s) isbetween

${{{ACOS}\left\lbrack \frac{A}{\sqrt{C^{2} + A^{2}}} \right\rbrack}{and}\pi} - {{{ACOS}\left\lbrack \frac{A}{\sqrt{C^{2} + A^{2}}} \right\rbrack}.}$

When φ=180 degrees the steerable antenna 154 is a linearly-polarizedmagnetic dipole with a slant angle

$\theta_{s} = {{ASIN}\left\lbrack \frac{C\left( {1 - B} \right)}{\sqrt{{C^{2}\left( {1 - B} \right)}^{2} + {A^{2}\left( {1 + B} \right)}^{2}}} \right\rbrack}$from the cylindrical axis of the steerable antenna 154, wherein A SIN( )is the inverse of sine function. The range of θ_(s) is between

${- {{ACOS}\left\lbrack \frac{A}{\sqrt{C^{2} + A^{2}}} \right\rbrack}}{and}{{{ACOS}\left\lbrack \frac{A}{\sqrt{C^{2} + A^{2}}} \right\rbrack}.}$By choosing φ to be either 0 or 180 degrees, the slant angle θ_(s) canbe made to be anywhere between

${{- {{ACOS}\left\lbrack \frac{A}{\sqrt{C^{2} + A^{2}}} \right\rbrack}}{and}\pi} - {{{ACOS}\left\lbrack \frac{A}{\sqrt{C^{2} + A^{2}}} \right\rbrack}.}$The entire range of the slant angle is 180 degrees. A linearly-polarizedmagnetic-dipole antenna in any direction in the X-Z plane can beembodied in the steerable antenna 154. For example, by setting B to be

$\frac{❘{C - A}❘}{C + A}$and φ to be 0 if A≥C or 180 degrees if A<C the steerable antenna 154depicted in FIG. 18 embodies a linear dipole antenna with a slant angleof 45 degrees from the cylindrical axis of the antenna segment.

A receiving linearly-polarized magnetic dipole antenna can be embodiedin a steerable antenna in the same way as a transmitting magnetic dipoleantenna with the same linear-polarization property. A set of (B, φ) thatmakes a transmitting steerable antenna a slant linearly-polarizedmagnetic dipole makes a receiving steerable antenna a magnetic dipolewith the same linear polarization and slant angle. As such, embodimentsherein can be applied to the steerable antenna to create an axialdipole, or a cross-axial dipole, or a slant linearly-polarized dipole,or an elliptically-polarized dipole receiver.

Embodiments herein can be used to construct a pure cross-axial antennawithout any axial component. FIGS. 19 and 20 illustrate an exemplarypure cross-axial antenna 156. The steel structure and other parts arevery similar to those of X-Z antenna combo 152 except only one arc wiresection 158 is provided. The steel structure is not shown in the figure.The ferrite rods (not shown) are placed in the cross-axial slots in thestraight sections and are sandwiched between the two wire segments ineach slot. There is no slot in the arc section of the wire. There is noaxial component in this design.

FIG. 20 shows the side view of the pure cross-axial antenna 156 in FIG.19 . The arc section of the wire-hole is embedded and can't be seen. Atuning circuit 112 is positioned in a tuning port 123, and accessedduring the construction process of the pure cross-axial antenna 156. Ametal cover may be used to protect the tuning port 123. Optional holes124 may be drilled radially inward from the sub surface to reach the arcwire section 158. During the manufacturing process, the holes 124 may beused to help threading antenna wire through the arc wire section 158.Then these holes 124 may be screwed or plugged with conducting material.These holes 124 are generally not functioning parts of the purecross-axial antenna 156 and may be used only during the manufacturingand maintenance phase, for example.

Measurements from a pair of axial transmitter-receiver antennas on a LWDtool are invariant under tool face rotation. The measurements can't beused to sense the azimuthal variations of formation properties aboutdrill string axis. Measurements from a pair of transmitter-receiverantennas where one antenna is axial and the other is cross-axial can besensitive to tool face angle of the cross-axial axis. Some azimuthalvariations of formation properties can be determined from themeasurements. If a formation is not azimuthally invariant, then thereceiver reading is a function of the tool face of the cross-axial axis.By measuring the tool face angle for each receiver reading, a receiverdata distribution can be obtained over tool face after the tool hasrotated at least 360 degrees. A transmitter-receiver antenna pair withboth being in cross-axial directions produces measurements sensitive toazimuthal variations of formation property.

Each resistivity measurement is made with a constant sampling window.Measurements are made on constant time-intervals. The rotational speedof a drill string can vary during drilling operations. A constant timeinterval between measurements does not translate into a constant toolface increment. The data distribution over tool face can be onunevenly-spaced tool face angles. For convenience of data processing andinterpretation, the data distribution over tool face is often obtainedor transformed into data on constantly-spaced tool face grids or bins.The transformation is accomplished by dividing the entire 0 to 360degree tool-face space into multiple equal-sized bins. A receiverreading is assigned to a bin where the tool face angle at the time ofthe reading lies. If multiple readings fall into a bin, then all thereadings in that bin are averaged into a reading for that bin. Aftermeasurement data has been collected for all bins, one set of datadistribution over tool face is obtained. The complete set of binned datamay be directly stored along with the time (cycle time) at the middle ofthe measurement cycle for the complete set of binned data. The set ofbinned data may be further processed and the results of processing alongwith the cycle time are stored in memory. Then, all bins are cleared forthe next set of distribution data. The variable drill-string rotationalspeed causes the measurement cycle to be variable. The measurement cycleis managed dynamically by resistivity tool's electronic system.

The measurement data distributions over tool face in binned format canbe directly used for an image log which is a two-dimensional plot overwell depth and tool face angle. A distribution over tool face is plottedat the average depth of a tool during the time period when data in allthe bins are collected for the distribution. The average depth is thetool depth at the cycle time. Time-to-depth correlation is performed bya logging system that includes a resistivity tool.

The frequencies used by LWD tools are much higher than the rotationalfrequency of a drill string during drilling process. For modeling toolresponse and data interpretation for a tool at a tool face angle, thetool may be considered to be stationary at that position.

Electromagnetic field generated by a transmitter on a wave propagationresistivity tool is a linear field and possesses the superpositionproperty. A cross-axial transmitter dipole is a vector in the X-Y planein a Cartesian coordinate system stationary with respect to Earth (wellframe) where z-axis is the cylindrical axis of the antenna cylinder anddrill string. At any tool face the dipole can be viewed as a vectorconsisting of two component vectors in the X and Y direction. The dipoleis the vector sum of the two component vectors. Namely the dipole vectoris given by{right arrow over (D)}(φ)=COS(φ)D{circumflex over (x)}+SIN(φ)Dŷ  (EQ.7),where φ is the tool face angle of the cross-axial transmitter, {rightarrow over (D)}(φ) is the transmitter dipole vector at tool face φ, D isthe dipole moment of the transmitter, {circumflex over (x)} and ŷ areunit vectors of the X and Y axes of the well frame, respectively.

The superposition principle dictates that the electromagnetic fieldgenerated by a cross-axial transmitter dipole at a tool face angle isthe same as the vector sum of fields separately generated by the twocomponent vectors, respectively. The axial component of the field on thez-axis some distance away measured by an axial dipole receiver isV(φ)=COS(φ)V _(zx)+SIN(φ)V _(zy)  (EQ. 8),where V(φ) is the complex receiver voltage representing phase andamplitude when the cross-axial transmitter is at tool face angle φ,V_(zx) and V_(zy) are axial receiver voltages when the tool face of thecross-axial transmitter are at zero and ninety degrees, respectively.

The receiver voltage of a cross-axial receiver on electromagnetic fieldgenerated by an axial transmitter dipole is also a simple sinusoidalfunction of tool face similar to that of EQ. 8.

The receiver measurement from an axial and cross-axialtransmitter-receiver pair varies with tool face as a sinusoidalfunction. As a Fourier series of tool face the measurement only has twonon-zero coefficients.

The measurement by a slanted linear magnetic dipole receiver onelectromagnetic field generated by a slanted linear magnetic dipoletransmitter is given by

$\begin{matrix}{{{V(\varphi)} = {\begin{bmatrix}{{{COS}\left( {\varphi + \varphi_{R}} \right)}{SIN}\left( \theta_{R} \right)} & {{SIN}\left( {\varphi + \varphi_{R}} \right){SIN}\left( \theta_{R} \right)} & {{COS}\left( \theta_{R} \right)}\end{bmatrix}*{\begin{pmatrix}V_{xx} & V_{xy} & V_{xz} \\V_{yx} & V_{yy} & V_{yz} \\V_{zx} & V_{zy} & V_{zz}\end{pmatrix}\begin{bmatrix}{{{COS}\left( {\varphi + \varphi_{T}} \right)}{{SIN}\left( \theta_{T} \right)}} \\{{{SIN}\left( {\varphi + \varphi_{T}} \right)}{{SIN}\left( \theta_{T} \right)}} \\{{COS}\left( \theta_{T} \right)}\end{bmatrix}}}},} & \left( {{EQ}.9} \right)\end{matrix}$where φ is tool face angle, (θ_(R),φ_(R)) are receiver slanted angle andtool face offset, (θ_(T),φ_(T)) are transmitter slanted angle and toolface offset, matrix element V_(ij) is the receiver voltage if thereceiver is in i-direction and the transmitter is in j-direction in awell frame.

The matrix V in EQ. 9 is termed the transfer matrix or transferfunction. It can be proven that the coefficients of Fourier transform ofV(φ) for third and all higher order harmonics in tool face angle φ arezero. There are at most five non-zero coefficients in a Fourier seriesfor receiver measurements over tool face for a pair of linear magneticdipole transmitter and receiver. Thus, the tool face variation of areceiver voltage can be characterized by a function with at most fivecomplex parameters. The minimum number of bins required for extractingthe five parameters is five.

With five bins, each bin spans seventy-two degrees in tool face. Thetool face angle of a piece of data may be anywhere within this tool faceinterval. The error from sampling jitter can be substantial (e.g.,thirty-six degrees in tool face). By using more bins than the necessary(e.g., minimum of five in the data binning process), the jitter error isreduced. Over-sampled data also reduces random measurement error.Increasing the number of bins will increase data storage requirement.The choice for the number of bins is a balance between minimizing jitterand random errors and minimizing data storage requirement.

In some embodiments, each bin is divided into multiple smaller sub-bins.After data for all the sub-bins in every bin are collected, the datacollection for one tool face distribution is deemed complete. The datafrom all the sub-bins in a bin are averaged or summed to be the data forthe bin. Only this data may be stored. As such, the sub-bin size limitsthe jitter error. The high number of sub-bins may also reduce randomerror. The small number of bins does not burden the data storage system.

In some embodiments, receiver measurement, as well as the tool faceangle at which the receiver measurement is made, is temporarily recordedduring the measurement process. After data has been collected for allthe bins, the complete set of binned data is either stored into memoryor processed into Fourier series coefficients (Fourier decomposition) tobe stored into memory. Since the tool face angles are not onuniformly-spaced grid, the Fourier decomposition is performed using atechnique designed for irregularly sampled data. As discussed herein,Fourier coefficients for third or higher order harmonics are zero formeasurement from each linear dipole transmitter-receiver pair. There areonly five non-zero coefficients. These five non-zero coefficients can bedetermined in a direct data-fitting optimization method such as theleast-squares. Since the precise value of the tool face angle associatedwith each receiver measurement is used there is no jitter error. Thenumber of bins or sub-bins does not have to be large to minimizingjitter error. A set of coarse bins can be used.

Random noise and other errors in binned data can cause the Fouriercoefficients for third and higher order harmonics to be non-zero. Thethird or higher order Fourier coefficients maybe computed and storedinto memory. The value of those coefficients can be used to gauge themeasurement quality of binned data.

Five or more measurements over tool face angle may be used to determinethe possible five non-zero Fourier coefficients. If the measurements areover a small range of tool face (azimuthal angle), then the underlineazimuthal variation to be measured may be small compared with the systemmeasurement error. The signal-to-noise ratio may be poor. By requiringmeasurement data present in each bin this problem is avoided in thisembodiment.

In a directional well gravity tool face is used for tool facemeasurement. It is given by:φ=A TAN 2(G _(y) ,−G _(x))  (EQ. 10)where G_(x) and G_(y) are gravity components in the cross-axial X and Ydirections in a Cartesian coordinate system fixed on the tool segment(sensor frame) with drill string axis as the Z-axis. The gravitycomponents are measured by accelerometers in a directional sensingsystem when the drill string is at rest. This is done during the pipechange period when a drill string segment is added to or removed fromthe drill string and the downhole section of the drill string is atrest.

In some embodiments, magnetic tool face is dynamically measured duringthe drilling process. Gravity tool face is obtained from the magnetictool face. Magnetic tool face is measured by magnetometers and themeasurement is unaffected during the drilling process by mechanicalfactors which destroy gravity measurements using accelerometers.Magnetic tool face φ_(m) isφ_(m) =A TAN 2(−M _(y) ,M _(x))  (EQ. 11)where M_(x) and M_(y) are Geomagnetic field components in X and Ycross-axial directions in the sensor frame, respectively.

The difference between magnetic and gravity tool faces φ−φ_(m) is afunction of the dip angle of the Geomagnetic field, the inclination andazimuth of the drill string segment where a directional sensor islocated. It is not a function of tool face. It is unchanged as the drillstring rotates if the attitude of the drill string remains the same. Inthis embodiment the instantaneous gravity tool face of the x-axis of amagnetometer used for the dynamic measurement of the Geomagnetic fieldis given by:φ=φ_(m)+(φ−φ_(m))_(Last Survey)  (EQ. 12),where φ and φ_(m) are the instantaneous gravity and magnetic tool faceswhile a drill string is rotating, (φ−φ_(m))_(Last survey) is thestationary gravity and Geomagnetic tool face difference obtained fromthe latest directional sensor survey conducted during a pipe changeperiod when the drill string is at rest. The approximation used inderiving EQ. 12 is that between two stationary surveys the attitude ofthe drill string and the well changes very little. The gravity tool faceerror associated with this approximation is much smaller than the toolface accuracy requirement for data binning.

The magnetometers used for dynamically measuring geomagnetic fieldcomponents in cross-axial directions during the drilling process may notbe the same ones used for stationary directional survey. The two sets ofcross-axial magnetometers maybe azimuthally misaligned about the drillstring axis. The EQ. 12 is still valid and may be used to obtain thegravity tool face angle of the cross-axial X-axis of the dynamicmagnetometer system.

The cross-axial component of a linear dipole antenna may be offset intool face from the X-axis of the sensor frame of a dynamic magnetometersystem. This offset is a known constant. The instantaneous gravity toolface of the cross-axial component of an linear dipole antenna is:φ_(g)=φ_(m)+(φ−φ_(m))_(Last Survey)+Δφ  (EQ. 13),wherein φ_(g) is the gravity tool face of the cross-axis of the antennaand Δφ is the tool face offset between the X axes of the antenna and thedynamic magnetometer system.

Directional sensor systems may be part of the electronic system of aresistivity tool with cross-axial antenna components. Cylindricalsections housing the directional sensor system may be part of aresistivity tool segment.

Prior art LWD tools with cross-axial antennas have been used to measureone or more parameters of formation properties. A LWD tool withcross-axial antennas using embodiments described herein can be moreefficient and more accurate than those of prior art.

Referring to FIGS. 8 and 21 , magnetic quadrupole antennas may be madewith embodiments described herein conveniently as compared to the priorart. For example, in FIG. 8 by crossing the wires (a half-turn twist) inthe wire hole diametrically opposite to a wire passageway 65 one obtainsan antenna with one half of the point dipoles pointing in the oppositedirection of the other half of point dipoles. The schematiccross-sectional view of an exemplary quadrupole antenna 160 is shown inFIG. 21 . The quadrupole antenna 160 is similar to FIG. 8 except thattwo wires segments 76 a and 77 a in the wire hole 31 a opposite to thewire passageway 65 is crossed at 128. The crossed section at 128 can beanywhere in that wire hole 31 a. It can also be in a portion of the slot15 a adjacent to the wire hole 31 a in FIG. 21 . The cross-axialdirection is shown as 126. The crossed section at 128 divides theferrite rod 33 a based dipoles into two groups. The left half of theferrite dipoles in FIG. 21 are 180 degrees out of phase with the righthalf. The total dipole moment is zero. The quadrupole moment is notzero. In a coordinate system where the Z-axis is the centerline of thesub cylinder, Y axis passes through the center of wire passageway 65 inFIG. 21 , and X-axis is pointing in the direction of 126, the X-Zcomponent of the quadrupole moment Q_(xz) is given approximately by:

$\begin{matrix}{{Q_{xz} = {\frac{2R}{\pi}dN}},} & \left( {{EQ}.14} \right)\end{matrix}$wherein R is the radial distance from the middle of the ferrite rod 33 ato the centerline of the steel sub, d is the axial magnetic dipolemoment of each ferrite rod 33 a construct, and N is the total number offerrite rods 33 a. The approximation used in obtaining EQ. 14 is that Nis assumed to be large so that the ferrite rod dipoles are assumed to beuniformly and continuously distributed circumferentially. For exactvalue the factor

$\frac{2R}{\pi}$in EQ. 14 is replaced by the average of the absolute values ofX-coordinates of all the ferrite rods 33 a in this coordinate system ifN is even and slots 15 a are uniformly distributed as shown in FIG. 21 .

The Z-X component Q_(zx) equals to Q_(xz) by the definition ofquadrupole moments. All other components of the quadrupole tensor arezero.

By crossing antenna wire segments in the wire hole 31 a notdiametrically opposite of wire passageway 65, the antenna includes botha dipole and quadrupole moment. Multiple antenna wire crossings can beused to create an antenna with non-zero dipole and quadrupole momentscentered on the cylindrical axis of a resistivity tool.

FIG. 22 shows the schematic wiring diagram of an exemplary quadrupoleantenna section 162 with cross-axial slots. The steel structure (notshown) with slots is almost identical to that of FIG. 20 . The ferriterods (not shown) are placed in the cross-axial slots in the straightsections and are sandwiched between the two wire segments in each slot.There is no slot in the arc section of the wire. Antenna wire 131 is acontinuous wire that may be similar to the antenna wire 115 in FIG. 19for pure cross-axial dipole antenna. Segments of the antenna wire 131are crossed in an arc section 164 of the wire hole as shown at 132. Thewire crossing 132 can be anywhere on the arc section 164 or thebeginning of one of the straight sections before the first ferrite rodnearest to the arc section 164. The wire crossing 132 causes the twogroups of ferrite dipoles on the two straight wire sections to be 180degrees in polarity from each other. The total dipole moment is zero. Ina coordinate system parallel to 133 with its origin located at thecenter between the two straight sections, the non-zero components of thequadrupole are:

$\begin{matrix}{{Q_{xy} = {Q_{yx} = {\frac{l}{2}dN}}},} & \left( {{EQ}.15} \right)\end{matrix}$wherein l is the distance between the two straight wire hole sections

$\left( \frac{l}{2} \right.$is the radius or antenna sub cylinder minus the depth of the centerlineof a ferrite rod from the sub surface), d is the dipole moment of aferrite rod construct in the direction of the rod (X direction incoordinate system 133), and N is the total number of cross-axial ferriterods in the two straight sections and is assumed to be even. All othercomponents of the quadrupole are zero.

In some embodiments, another wire crossing similar to wire crossing 132in FIG. 22 can be positioned to create two groups of dipoles where thenumbers of slot based dipoles in them are unequal. The dipoles in eachgroup are in phase and the two groups are 180 degrees out of phase. Thetotal dipole moment is not zero. The antenna possesses both dipole andquadrupole moments. As in the case with axial dipoles, multiple wirecrossings 132 can be used in an embodiment to create an antenna with allthe moments centered on the resistivity tool cylindrical axis.

In prior art, the orientation of a wire hole section is importantbecause a single wire segment in the section induces current around thewire hole structure and the induced current becomes an active part of anantenna. Antenna structures using embodiments described herein do nothave strict requirements on the orientation of wire holes since thereare two wire segments in a wire hole and the net current of the twosegments is zero. Wire segments in wire holes do not participate in thetransmitting or receiving function of an antenna built withinembodiments described herein. The angle at which a wire segment crossingor passing through a ferrite rod may influence an antenna's behavior.Hereafter, unless specified otherwise it is assumed that a wire passesover/under a ferrite rod at a right angle to the major axis of theferrite rod.

The two wire segments in a wire hole can be twisted a number of completeturns without altering the polarity of dipoles. A half-turn twistcrosses the two wire segments and causes a polarity change in adjacentslots. It is understood that two wire segments maybe twisted in a wirehole to minimize any magnetic moment from the two segments.

Referring to FIG. 23 , the operation of a resistivity tool is managed bya transceiver electronic system 165. The transceiver electronic system165 is housed in the tool's drill collar segments. The transceiverelectronic system 165 may include an electronic control unit 166, areceiver electronic unit 167, and a transmitter electronic unit 168.Antenna tuning and signal measurement electronics of receivers are partof the receiver electronic unit 167. Receiver antennas 175 are connectedto the receiver electronic unit 167 by electric wires 172. Theelectronic control unit 166 powers, controls, and collects receivermeasurements from the receiver electronic unit 167 via an electricconnection system 170. The electronic control unit 166 powers andcommands the transmitter electronic unit 168 by a connection system 171.The transmitter electronic unit 168 comprises tuning circuits and othertransmitter electronics. The transmitter electronic unit 168 powerstransmitter antennas 176 by a connection system 173. FIG. 23 is aschematic functional diagram. In some embodiments, part of or the wholeelectronic control unit 166 and the receiver electronic unit 167 may befabricated on a single electronic board. Part of transmitter electronicunit 168 may be on an electronic board where majority of the electronicsfor the electronic control unit 166 reside. In some embodiments, antennatuning circuits of the receiver electronic unit 167 or transmitterelectronic unit 168 are located next to the antennas 175 and 176 and arenot on the electronic board for the rest of the unit which they are partof.

The electronic control unit 166 may connect to the rest of the downholesystem via a connection system 169. The electronic control unit 166 mayinclude a directional sensing subsystem. The transceiver electronicssystem 165 and antennas 175 and 176 may be housed in different sectionsof drill collars. Hereinafter, the collection of all the sections ofdrill collars for housing all the components of a resistivity tool maybe called a drill collar segment.

It should also be understood that embodiments described herein alsodescribe that wherein passing over/under a ferrite rod in a slot, a wiremay wrap around the rod one or more times before leaving the slot. Wiretwisting in a wire hole and wire wrapping of a ferrite rod in a slot maynot change that the net current in a wire hole is zero and the netcurrent forms complete loops around a ferrite rod.

Furthermore a ferrite or a ferrite rod may be made of a single volume ofmagnetic material or may consist of several pieces linearly concatenatedtogether or packed in parallel.

While some embodiments have been shown and described, variousmodifications and substitutions may be made without departing from thespirit and scope of the invention.

Techniques for providing one or more antennae within a drilling assemblyare disclosed in the following references, which are hereby incorporatedby reference in their entirety:

-   U.S. Pat. No. 5,001,675 (March 1991), Woodward;-   U.S. Pat. No. 5,138,263 (August 1992), Towle;-   U.S. Pat. No. 5,331,331 (July 1994), Wu;-   U.S. Pat. No. 5,491,488 (February 1996), Wu;-   U.S. Pat. No. 5,530,358 (June 1996), Wisler, et al.;-   U.S. Pat. No. 6,181,138 (January 2001), Hagiwara;-   U.S. Pat. No. 6,163,155 (December 2000), Bittar;-   U.S. Pat. No. 8,378,908 (February 2013), Wisler, et al.;-   U.S. Pat. No. 8,471,563 (June 2013), Wisler, et al.;-   U.S. Pat. No. 8,604,796 (December 2013), Wisler, et al.;-   U.S. Pat. No. 9,140,817 (September 2015), Wisler, et al.;-   U.S. Pat. No. 9,366,780 (June 2016), Wisler, et al.; and,-   U.S. Pat. No. 9,885,800 (February 2018), Wisler, et al.

What is claimed is:
 1. An electromagnetic wave propagation toolcomprising: a drill collar segment having an outer surface; an antennasystem disposed on the drill collar segment, the antenna systemincluding at least one transmitter antenna and at least one receiverantenna, at least one of the transmitter antenna or the receiver antennain the antenna system being a magnetic dipole based antenna comprisingslot based magnetic dipoles, the slot based magnetic dipoles comprising:at least one wire hole positioned beneath the outer surface of the drillcollar segment; at least two slots positioned in the outer surface ofthe drill collar, the at least one wire hole connecting a plurality ofslots with each other; a ferrite rod placed in each slot; and, acontinuous antenna wire passing through slots and wire holes via a firstroute, the continuous wire turning around and repassing through theslots and the wire holes via a second route such that two wire segmentsin each slot are positioned above and below each ferrite rod; atransceiver electronics system disposed on the drill collar segment, thetransceiver electronics system including a receiver electronics unit, atransmitter electronics unit, and an electronic control unit, theelectronic control unit including electronic hardware, software, andfirmware for scheduling and managing measurement sequence at at-leastone frequency and for processing receiver data into output; and, whereinthe at least one wire hole further connect slots with the transceiverelectronics system, the continuous wire further connects with thetransceiver system through the wire holes.
 2. The electromagnetic wavepropagation tool of claim 1, wherein the magnetic dipole antenna is atransmitter antenna.
 3. The electromagnetic wave propagation tool ofclaim 1, wherein the magnetic dipole antenna is a receiver antenna. 4.The electromagnetic wave propagation tool of claim 1, wherein the slotsand slot based magnetic dipoles are in an axial direction and aresubstantially uniformly distributed azimuthally about an axis of thedrill collar segment, the slot based magnetic dipoles being at one axiallocation on the drill collar segment and are in phase forming acollective axial antenna.
 5. The electromagnetic wave propagation toolof claim 1, wherein the slots and slot based magnetic dipoles are in anaxial direction and are substantially uniformly distributed azimuthallyabout an axis of the drill collar segment, the magnetic dipoles being atone axial location on the drill collar segment, wherein the continuouswire is arranged such that two groups of slot based dipoles are formed,the magnetic dipoles in each group are in phase and the two magneticdipole groups are 180 degrees out of phase.
 6. The electromagnetic wavepropagation tool of claim 1, wherein slots and slot based magneticdipoles are in an axial direction and are disposed into three groupsazimuthally distributed about an axis of the drill collar segment, themagnetic dipoles being at one axial location on the drill collarsegment.
 7. The electromagnetic wave propagation tool of claim 1,wherein the slots and slot based magnetic dipoles are parallel in across-axial direction and are in phase forming a collective cross-axialantenna, the transceiver electronic system further comprising asubsystem for obtaining a tool face angle of the cross-axial axis. 8.The electromagnetic wave propagation tool of claim 7, wherein the slotbased magnetic dipoles are disposed into two axially distributed groupswherein the two axially distributed groups are 180 degrees apartazimuthally about a center axis of the drill collar segment.
 9. Theelectromagnetic wave propagation tool of claim 1, wherein the slots andslot based magnetic dipoles are in a cross-axial direction, and whereinthe continuous wire is arranged such that two dipole groups of slotbased magnetic dipoles are formed, the slot based magnetic dipoles ineach group are in phase and the two dipole groups are 180 degrees out ofphase.
 10. The electromagnetic wave propagation tool of claim 1, whereinthe slot based magnetic dipoles consist of two groups with a first groupconsisting of axial slot based dipoles and a second group consisting ofcross-axial slot based dipoles in a cross-axial direction and are inphase, forming a collective slant antenna; and wherein the transceiverelectronics system further comprises a subsystem for obtaining a toolface angle.
 11. The electromagnetic wave propagation tool of claim 10,wherein the first group of axial slot based dipoles are disposed at twoaxial dipole locations on the drill collar segment and the second groupof cross-axial slot based dipoles are disposed on the drill collarsegment in between the two axial dipole locations so that a center ofcollective axial dipole moment coincides with a center of collectivecross-axial dipole moment.
 12. The electromagnetic wave propagation toolof claim 10, wherein the transceiver electronics system furthercomprises subsystems for dividing face space of the electromagnetic wavepropagation tool into several bins and collecting and averaging receiverdata in each bin.
 13. The electromagnetic wave propagation tool of claim12, wherein the transceiver electronics system further comprisessubsystems for processing binned data into a data distribution over toolface angle.
 14. The electromagnetic wave propagation tool of claim 12,wherein the transceiver electronics system further comprises subsystemsfor processing binned data into a parameter indicative of formationazimuthal properties.
 15. The electromagnetic wave propagation tool ofclaim 12, wherein the transceiver electronics system further comprisessubsystems for transforming binned data into coefficients of a Fourierseries of tool face angle.
 16. An electromagnetic wave propagation toolcomprising: a drill collar segment; an antenna system disposed on anouter surface of the drill collar segment, the antenna system comprisingat least one transmitter antenna and at least one receiver antenna; atransceiver electronics system disposed on the drill collar segment, thetransceiver electronics system comprising a receiver electronics unit, atransmitter electronics unit, and an electronic control unit, theelectronic control unit comprising electronic hardware, software, andfirmware for scheduling and managing measurement sequence at at-leastone frequency and for processing receiver data into output; wherein atleast one of the transmitter antenna or the receiver antenna in theantenna system is a magnetic dipole based antenna comprising: aplurality of slot based magnetic dipoles comprising two, or more slotsin the outer surface of the drill collar segment and wire holes beneaththe outer surface, the wire holes connecting adjacent slots, and slotswith the transceiver electronics system; ferrite rods positioned in theplurality of slots; a first continuous antenna wire routed through afirst set of the slots via the wire holes in a first route and turnsaround to repass through the first set of the slots and wire holes via asecond route, wherein two wire segments of the first continuous wire ineach slot are positioned above and below each ferrite rod within eachslot, the first continuous wire further connecting to and from thetransceiver electronic system; a second continuous antenna wire routedthrough a second set of the slots via the wire holes in a third routeand turns around to repass through the second set of slots and wireholes in a fourth route, wherein two wire segments of the secondcontinuous wire in each slot are positioned above and below each ferriterod within each slot, the second continuous wire further connecting toand from the transceiver electronic system; and, wherein the transceiverelectronics system further comprises a subsystem that maintains relativeamplitude and phase between currents in the first continuous wire andthe second continuous wire.
 17. The electromagnetic wave propagationtool of claim 16, wherein the magnetic dipole based antenna is atransmitter antenna.
 18. The electromagnetic wave propagation tool ofclaim 16, wherein the magnetic dipole based antenna is a receiverantenna.
 19. The electromagnetic wave propagation tool of claim 16,wherein relative amplitude and phase between the first and secondcontinuous wires results in an axial dipole antenna.
 20. Theelectromagnetic wave propagation tool of claim 16, wherein relativeamplitude and phase between the first and second continuous wiresresults in a cross-axial dipole antenna.
 21. The electromagnetic wavepropagation tool of claim 16, wherein: the slots and wire holes are in asteerable antenna pattern; the first and second continuous wires followsteerable antenna routes; and, the transceiver electronics systemfurther comprises a subsystem for obtaining a tool face.
 22. Theelectromagnetic wave propagation tool of claim 21, wherein the relativeamplitude and phase between the first and second continuous wiresresults in a slanted dipole antenna between axial and cross-axialdirections.
 23. The electromagnetic wave propagation tool of claim 22,wherein the transceiver electronics system further comprises subsystemsfor dividing face space into several bins and collecting and averagingreceiver data in each bin.
 24. The electromagnetic wave propagation toolof claim 23, wherein the transceiver electronics system furthercomprises subsystems for processing binned data into a data distributionover tool face angle.
 25. The electromagnetic wave propagation tool ofclaim 23, wherein the transceiver electronics system further comprisessubsystems for processing binned data into a parameter indicative offormation azimuthal properties.
 26. The electromagnetic wave propagationtool of claim 23, wherein the transceiver electronics system furthercomprises subsystems for transforming binned data into coefficients of aFourier series of tool face angle.